On the unexplored relationship between kinetic energy and helicity in prosthetic heart valves hemodynamics

Surgical replacement of the diseased aortic valve consists in the implantation of a prosthetic heart valve (PHV), either biological or mechanical (BHV and MHV, respectively). Risks of complication have been linked to high levels of turbulence and consequent energy dissipation induced by the PHV. As helicity is an emergent feature in cardiovascular flows, deemed to impact blood flow organization, stability and the turbulent energy cascade, in this study the interplay between the production/decay of phase-averaged and turbulent kinetic energy and helicity in the presence of a BHV or MHV was investigated. Technically, direct numerical simulations of the coupled fluid-structure interaction problem were conducted using the immersed boundary method. A quantitative description of phase-averaged and fluctuating helicity, mean and turbulent kinetic energy was adopted to explore the nature of the kinetic energy vs. helicity relationship. A clear PHV-type dependence of the helicity production/decay in the downstream hemodynamics emerged, with MHVs hemodynamics presenting larger phase-averaged and fluctuating helicity than BHVs. For both heart valve types strong linear correlations were found between volume-average kinetic energy and helicity when based on phase-averaged or fluctuating quantities (Pearson's correlation coefficient r up to 0.98, p<0.001). The generation of turbulent kinetic energy or fluctuating helicity for both heart valve types was delayed with respect to the inflow waveform or the generation of both mean kinetic energy and phase-averaged helicity (up to 5.4% of the cardiac cycle). The exploration of the link between helical and turbulent hemodynamic flow features expands the current understanding of the PHV hemodynamic features associated with clinical complications, potentially translating into improvements of the design of PHVs.